the cheapest way i can think of is for you to hop on the florence bus (go to the train station and get on #7) that heads up to fiesole and spend the day exploring this ancient etruscan village.
take along a guide book and map because there is a lot to see and learn about.
there's also some vineyards that the locals will direct you to and you can enjoy some free wine tastings. and olive oil, if you like.
enjoy a nice dinner at la reggia ristorante and watch the sunset before you jump back on the bus to return to florence.
it will be a beautiful and affordable day.